Quadratic Programming Model for Stable Electricity Market Clearing
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing electricity market models face issues with multiplicity and instability of market clearing prices, leading to incorrect price signals and significant variations, which impact bilateral trades and the reliability of energy delivery.
Innovation Solution
Incorporating market clearing price variables into a quadratic programming model with relaxation of pricing constraints and adding a sum of squares term to the objective function, ensuring unique and stable market clearing prices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a bid-based security constrained economic dispatch model is used to determine market clearing prices, then the market can clear trades efficiently, but the model produces multiple possible market clearing prices leading to instability and incorrect price signals
Solution Approach 1:
The patent changes the mathematical formulation of the economic dispatch model by introducing a quadratic objective function that minimizes the sum of squared differences between offered prices and market clearing prices. This parameter change transforms the model from producing multiple discrete price solutions to producing a single continuous price solution, thereby resolving the instability and multiplicity problem while maintaining market clearing efficiency
Solution Approach 2:
The patent introduces an intermediary variable representing the market clearing price that acts as a mediator between supply bids and demand offers. This intermediary is determined through optimization rather than simple matching, providing a stable and unique price signal that resolves the contradiction between efficient market clearing and price stability
2Measurement precision
If locational marginal pricing is used to calculate shadow prices at each node, then theoretical pricing is achieved, but small variations in supply and demand cause significant price fluctuations
Solution Approach 1:
The patent modifies the pricing model by changing from linear marginal pricing to quadratic pricing optimization. This parameter change makes the price determination less sensitive to small variations in supply and demand by minimizing squared deviations, thereby reducing price volatility while maintaining accurate reflection of supply-demand conditions
Data Source
AI summary
Embodiments provide systems and methods for operating a power system to deliver energy. Embodiments include receiving constraints within a scheduling and pricing system; receiving bids with corresponding generation capacity and offers with corresponding load requirements, within the scheduling and pricing system; applying the constraints, the bids, the generation capacity, the offers, and the load requirements to a quadratic programming model of a market clearing system within the scheduling and pricing system; determining market clearing prices and corresponding generation and load schedules based on optimizing the quadratic programming model of a market clearing system; distributing the market clearing prices and corresponding generation and load schedules to a billing and settlement system; distributing the generation and load schedules to a generation control and load management system; and directing operation of generator resources and managing loads to deliver energy to customers based on the generation and load schedules. Numerous other aspects are provided.